In a class of 25 students, 18 were math majors, 12 were computer science majors, and 7 were dual majors in math and computer science. How many students were majoring in math only? How many students were majoring in Computer Science only? How many students were not math or computer science majors?

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.